Heat Generation by Electric Current in a Quantum Dot Molecular Coupled to Ferromagnetic Leads

Abstract

We study the properties of the heat flow generated by electric current in a quantum dot (QD) molecular sandwiched between two ferromagnetic leads. The heat is exchanged between the QD and the phonon reservoir coupled to it. We find that when the leads' magnetic moments are in parallel configuration, the total heat generation is independent on the leads' spin-polarization regardless of the magnitude of the intradot Coulomb interaction. This behavior is similar to that of the electronic current. In the antiparallel configuration, however, the influences of the leads' ferromagnetism on the heat generation are quite different from those on the electric current. Under the conditions of weak intradot Coulomb interaction and small bias voltage, the heat generation is monotonously suppressed by increasing leads' spin-polarization. Whereas for sufficient large intradot Coulomb interaction and bias voltage, the heat generation shows non-monotonous behavior due to the electron-phonon interaction and the spin accumulation induced on the dot. Furthermore, the magnitude of the negative differential of the heat generation previously found in a QD connected to nonmagnetic leads can be weakened by the increase of the spin-polarization of the ferromagnetic leads.

Spin Effects on Heat Current Through a Quantum Dot Attached to Ferromagnetic Leads

“…Moreover, the central position of the two peaks move, respectively, toward μ +hω q /2 and −(U +hω q /2) with reduced widths. This non-monotonous variation of the heat generation with, respectively, to the ferromagnetism on the leads has been found in previous work, in which the electrons are driven by the usual electric bias [51].…”

“…The dot single-electron Green's functionsG r,a,<,> σ (ω) are the Fourier transforms ofG r,a,<,> σ (t) defined in terms of Hamiltonian (2), i.e., the retarded [50]. By employing the equation of motion technique, the retarded Green's function is obtained as [31,50,51]…”

“…Here as an equivalent choice, we assume square bands of both spin-up and spin-down electrons (wide band approximation) and assume spin-dependent tunneling matrix V kβσ . The spin-dependent line-width function βσ is defined in terms of a spin-polarization parameter P β in each lead as [51] P β = ( β↑ − β↓ )/( β↑ + β↓ ), or βσ = β0 (1 + σ P β ) with β0 = ( β↑ + β↓ )/2 [24,25]. For parallel configuration, we have P L = P R = P, and P L = −P R = P for antiparallel configuration.…”

Enhanced heat rectification effect in a quantum dot connected to ferromagnetic leads

“…In their work, the heat is generated due to the EPI, through which the energy associated with the electric current in central region is transferred to the phonon bath in the form of heat. They demonstrated that the law of the heat generation in macroscopic system, i.e., the Joule law, breaks down in zero-dimensional quantum-dot (QD) system and some unique behaviors of the heat current were predicted [13,14,[20][21][22][23][24][25][26][27]. For example, resonant phonon emitting occurs when the modified intradot Coulomb interaction is equal to the phonon energy, giving rise to a huge peak in heat generation despite a very weak electric current [14].…”

“…[29]. It should be noted that the electron spin degree of freedom has not attracted much attention in those previous works concerning heat generation or thermal diode [13,14,[20][21][22][23][24][25][26][27]. Recently, we studied the heat generation in a system composed of a QD connected to ferromagnetic leads, and found that the ferromagnetism of the external leads will influence the heat generation and the electric current in different ways.…”